Special semi-reducible pseudo-Riemannian spaces

Abstract


 The paper contains necessary conditions allowing to reduce matrix tensors of pseudo-Riemannian spaces to special forms called semi-reducible, under assumption that the tensor defining tensor characteristic of semireducibility spaces, is idempotent.
 The tensor characteristic is reduced to the spaces of constant curvature, Ricci-symmetric spaces and conformally flat pseudo-Riemannian spaces.
 
 The obtained results can be applied for construction of examples of spaces belonging to special types of pseudo-Riemannian spaces.
 
 The research is carried out locally in tensor shape, without limitations imposed on a sign of a metric.
 

On conformally reducible pseudo-Riemannian spaces

“…A space V n is called a conformally reducible, whenever its metric in a certain holonomic system of coordinates takes the following form, [2,4,18]:…”